This study proposes a real-time rendering algorithm for lighting when each of more than 100,000 moving particles exists as a light source. Two 3D textures are used to dynamically determine the range of influence of each light, and the first 3D texture has light color and the second 3D texture has light direction information. Each frame goes through two steps. The first step is to update the particle information required for 3D texture initialization and rendering based on the Compute shader. Convert the particle position to the sampling coordinates of the 3D texture, and based on this coordinate, update the colour sum of the particle lights affecting the corresponding voxels for the first 3D texture and the sum of the directional vectors from the corresponding voxels to the particle lights for the second 3D texture. The second stage operates on a general rendering pipeline. Based on the polygon world position to be rendered first, the exact sampling coordinates of the 3D texture updated in the first step are calculated. Since the sample coordinates correspond 1:1 to the size of the 3D texture and the size of the game world, use the world coordinates of the pixel as the sampling coordinates. Lighting process is carried out based on the color of the sampled pixel and the direction vector of the light. The 3D texture corresponds 1:1 to the actual game world and assumes a minimum unit of 1m, but in areas smaller than 1m, problems such as stairs caused by resolution restrictions occur. Interpolation and super sampling are performed during texture sampling to improve these problems. Measurements of the time taken to render a frame showed that 146 ms was spent on the forward lighting pipeline, 46 ms on the defered lighting pipeline when the number of particles was 262144, and 214 ms on the forward lighting pipeline and 104 ms on the deferred lighting pipeline when the number of particle lights was 1,024766.
Internet commerce has been growing at a rapid pace for the last decade. Many firms try to reach wider consumer markets by adding the Internet channel to the existing traditional channels. Despite the various benefits of the Internet channel, a significant number of firms failed in managing the new type of channel. Previous studies could not cleary explain these conflicting results associated with the Internet channel. One of the major reasons is most of the previous studies conducted analyses under a specific market condition and claimed that as the impact of Internet channel introduction. Therefore, their results are strongly influenced by the specific market settings. However, firms face various market conditions in the real worlddensity and disutility of using the Internet. The purpose of this study is to investigate the impact of various market environments on a firm's optimal channel strategy by employing a flexible game theory model. We capture various market conditions with consumer density and disutility of using the Internet.
shows the channel structures analyzed in this study. Before the Internet channel is introduced, a monopoly manufacturer sells its products through an independent physical store. From this structure, the manufacturer could introduce its own Internet channel (MI). The independent physical store could also introduce its own Internet channel and coordinate it with the existing physical store (RI). An independent Internet retailer such as Amazon could enter this market (II). In this case, two types of independent retailers compete with each other. In this model, consumers are uniformly distributed on the two dimensional space. Consumer heterogeneity is captured by a consumer's geographical location (ci) and his disutility of using the Internet channel (${\delta}_{N_i}$).
shows various market conditions captured by the two consumer heterogeneities.
(a) illustrates a market with symmetric consumer distributions. The model captures explicitly the asymmetric distributions of consumer disutility in a market as well. In a market like that is represented in
(c), the average consumer disutility of using an Internet store is relatively smaller than that of using a physical store. For example, this case represents the market in which 1) the product is suitable for Internet transactions (e.g., books) or 2) the level of E-Commerce readiness is high such as in Denmark or Finland. On the other hand, the average consumer disutility when using an Internet store is relatively greater than that of using a physical store in a market like (b). Countries like Ukraine and Bulgaria, or the market for "experience goods" such as shoes, could be examples of this market condition.
summarizes the various scenarios of consumer distributions analyzed in this study. The range for disutility of using the Internet (${\delta}_{N_i}$) is held constant, while the range of consumer distribution (${\chi}_i$) varies from -25 to 25, from -50 to 50, from -100 to 100, from -150 to 150, and from -200 to 200.
summarizes the analysis results. As the average travel cost in a market decreases while the average disutility of Internet use remains the same, average retail price, total quantity sold, physical store profit, monopoly manufacturer profit, and thus, total channel profit increase. On the other hand, the quantity sold through the Internet and the profit of the Internet store decrease with a decreasing average travel cost relative to the average disutility of Internet use. We find that a channel that has an advantage over the other kind of channel serves a larger portion of the market. In a market with a high average travel cost, in which the Internet store has a relative advantage over the physical store, for example, the Internet store becomes a mass-retailer serving a larger portion of the market. This result implies that the Internet becomes a more significant distribution channel in those markets characterized by greater geographical dispersion of buyers, or as consumers become more proficient in Internet usage. The results indicate that the degree of price discrimination also varies depending on the distribution of consumer disutility in a market. The manufacturer in a market in which the average travel cost is higher than the average disutility of using the Internet has a stronger incentive for price discrimination than the manufacturer in a market where the average travel cost is relatively lower. We also find that the manufacturer has a stronger incentive to maintain a high price level when the average travel cost in a market is relatively low. Additionally, the retail competition effect due to Internet channel introduction strengthens as average travel cost in a market decreases. This result indicates that a manufacturer's channel power relative to that of the independent physical retailer becomes stronger with a decreasing average travel cost. This implication is counter-intuitive, because it is widely believed that the negative impact of Internet channel introduction on a competing physical retailer is more significant in a market like Russia, where consumers are more geographically dispersed, than in a market like Hong Kong, that has a condensed geographic distribution of consumers.